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Fluid Structure Interaction

PVP2006-ICPVT-11-93013 pp. 5-13; (9 pages)
doi:10.1115/PVP2006-ICPVT-11-93013

The present paper exposes a homogenization method developed in order to perform the modal analysis of a nuclear reactor with fluid-structure interaction effects. The homogenization approach is used in order to take into account the presence of internal structures within the pressure vessel. A homogenization method is proposed in order to perform a numerical calculation of the frequencies and modal masses for the eigenmodes of the coupled fluid-structure problem. The technique allows the use of a simplified fluid-structure model that takes into account the presence of internal structures: the theory bases are first recalled, leading to a new formulation of the fluid-structure coupled problem. The finite element discretization of the coupled formulation leads to the modification of the classical fluid-structure interaction operators. The consistency of the formulation is established from a theoretical point of view by evaluating the total mass of the coupled system with the fluid and structure mass operator, and the modified added mass operator. The method is tested and validated on a 2D case (two concentric cylinders with periodical rigid inclusions within the annular space) and applied on the industrial case. A complete modal analysis (calculation of frequencies and modal masses) is performed on a simplified geometry of a nuclear reactor with and without internal structures. Numerical results are then compared and discussed, and the influence of the internal structures on the fluid-structure coupled phenomenon is highlighted.

PVP2006-ICPVT-11-93014 pp. 15-24; (10 pages)
doi:10.1115/PVP2006-ICPVT-11-93014

The present paper deals with numerical analysis of fluid-structure interaction problems with commercial finite element codes. The various fluid-structure formulations are today well known from a theoretical point of view, but their application to the dynamic analysis of industrial problems with spectral methods can not be performed with all available codes. The present study exposes a developing process currently undertaken in order to integrate symmetric FSI formulation within the commercial finite element code Ansys. This process is carried out in several steps which are detailed here: first, on overview of the existing fluid-structure formulations is exposed with the view to comparing various finite element codes. Then, coupled symmetric and non-symmetric formulations are recalled on two general FSI problems (elasto-acoustic and hydro-elastic problems) and applied on a generic reference test case. Numerical integration of the presented methods is performed on the Ansys code in the following direction: free surface condition for sloshing mode in pressure formulation, harmonic axi-symmetric pressure fluid formulation for coupled axi-symmetric calculations, general symmetric coupled formulation in u ,p,φ (for elasto-acoustic problems with fluid free surface without sloshing) and u ,p,η (hydro-elastic problems with fluid free surface with sloshing) formulations. Elementary validations of the implemented methods are proposed by comparing Ansys numerical results to calculations results obtained with a finite element code developed by DCN Propulsion, and presented in the paper. All the developments will be available in future release of the Ansys code in the coming years for the benefit of the Ansys users’ community.

PVP2006-ICPVT-11-93015 pp. 25-33; (9 pages)
doi:10.1115/PVP2006-ICPVT-11-93015

The present paper deals with the modal analysis of a nuclear with fluid-structure interaction effects. In a previous study, added mass and added stiffness effects due to fluid-structure interaction were modeled and studied. A dynamic analysis was performed for a seismic excitation, i.e. in the low frequency range. The present study deals with high frequency analysis, i.e. taking into account compressibility effects in the fluid problem. Elasto-acoustic coupling phenomena are studied and described in the industrial case. The elasto-acoustic coupled problem is formulated using the displacement/pressure-displacement potential coupled formulation which yields symmetric matrices. A modal analysis is first performed on the fluid problem alone, with a calculation of acoustic eigenfrequencies and the corresponding modal masses. A modal analysis is then performed for the coupled fluid-structure problem in the case of an incompressible fluid and a compressible fluid at standard pressure and temperature conditions and for a compressible fluid at the operating pressure and temperature conditions. Elasto-coupling effects are then highlighted and discussed.

PVP2006-ICPVT-11-93016 pp. 35-44; (10 pages)
doi:10.1115/PVP2006-ICPVT-11-93016

The present paper deals with the study of fluid forces in an incompressible viscous fluid at rest around an accelerated rigid circular cylinder. The movement subjected to the cylinder is an impulsive motion represented by a only one period of a sinusoidal acceleration. After this period, the cylinder is stopped. This study is performed for small displacement of the cylinder, i.e. for low KEULEGAN-CARPENTER numbers, and for various STOKES numbers. An analytical formulation of fluid forces exerted on a cylinder subjected to any motion is first proposed. The starting point of the analytical approach is the solution of fluid forces in steady state harmonic motion. A Fourier transform is applied on the harmonic solution to capture the wide frequency spectrum composing the transient motion. Then an inverse Fourier transform is applied on the expression to achieve the solution in the temporal space. A numerical simulation is then carried out with a CFD code using finite volume method with moving mesh technique in ALE formulation. The analytical and numerical solutions are exposed and discussed in the case of a cylinder subjected to a sine wave acceleration. The competition between the viscous diffusion time and the wave duration time is studied and highlights the history effect on pressure forces and shear forces.

PVP2006-ICPVT-11-93017 pp. 45-54; (10 pages)
doi:10.1115/PVP2006-ICPVT-11-93017

This paper deals with fluid forces induced by an oscillating rigid circular cylinder in a fluid initially at rest. The amplitude of the imposed movement is assumed sufficiently small so that no wake is formed. The objective of the present paper is to review different theoretical methods to evaluate fluid forces. A wide variety of conditions is considered, from inviscid, compressible flows in infinite fluid domains, to viscous, incompressible and strongly confined ones. A special care is taken to underline the limits of the simplified models regarding real fluid effects, such as three-dimensional centrifugal instabilities. This review is related to a study whose ultimate aim is to predict dynamic fluid load during a typical shock encountered in the environment of a military ship.

PVP2006-ICPVT-11-93018 pp. 55-61; (7 pages)
doi:10.1115/PVP2006-ICPVT-11-93018

The study of a interaction fluid-structure problem requires the calculation of fluid forces acting on moving boundaries. Since the first studies carried out by Stokes, a lot of work has been performed to derive various expressions of fluid forces, in particular for the case of simple geometry, such as infinite planes, spheres or circular cylinders. These bodies are subjected to elementary motions, namely harmonic motions or Dirac acceleration motions, (i.e. constant speed velocity motions). The present paper exposes a review of fluid forces exerted on accelerated rigid body in an incompressible viscous fluid initially at rest. The principal objective of this paper is to carry out a synthesis of the current literature and to develop a general analytical formulation of the fluid forces in order to deal with more general rigid body motions. The analytical formulation is exposed in the present paper for fluid forces acting on any moving body. This approach is limited to low displacements of the solid body, i.e. the non linear convective term of NS equation is not taken into account. The non-dimensional numbers is pointed out and detailed. The different solutions given in the literature are especially discussed with the influence of the viscosity compared to the irrotational model.

Topics: Force , Fluids
PVP2006-ICPVT-11-93051 pp. 63-72; (10 pages)
doi:10.1115/PVP2006-ICPVT-11-93051

This paper is related to the fluid forces prediction on a rapidly moving circular cylinder in cylindrical confinement. The Fritz model, which mainly assumes infinitesimal motions of the inner cylinder in an inviscid fluid, is one of the simplest model available in the scientific literature and is often used by design engineers in the nuclear industry. In this paper, simple non-linear expressions of fluid forces are derived for the case of finite amplitude motions of the inner cylinder. Assuming a potential flow, advection term and geometrical deformations can be taken into account. The problem, formulated as a boundary-perturbation problem, is solved thanks to a regular expansion. The range of validity of the approximate analytical solution thus obtained is theoretically discussed. The results are also confronted to numerical simulations, which allows to emphasize some limits and advantages of the analytical approach.

PVP2006-ICPVT-11-93108 pp. 73-79; (7 pages)
doi:10.1115/PVP2006-ICPVT-11-93108

The aim of this study is to estimate residual stresses and distortions during the assembly of dissimilar metallic materials welded by Electron Beam Welding (EBW) technique. This work is motivated by a new welding procedure for the manufacture of large speed reduction gear. The gear consists of a central hub of S275 J2G3 steel and a toothed wheel of 32CrMoV13 steel, chosen for its high fatigue performances. Preliminary experimental welding tests have shown the opening of the joint plane during the circular welding of the gear leading to lack-of-fusion defects. To improve the joining technique, a thermomechanical model has been developed to predict the opening of the joint plane during welding. A two-dimensional finite element model has been applied on a simplified geometry of smaller size. The opening of the joint plane has been modelled by two different ways, the first one uses activation / deactivation elements and the second one uses specific contact elements. Both techniques have shown similar displacements. The assumptions of plane stress or generalized plane strain are discussed. Numerical results obtained with similar metals with or without metallurgical transformations are presented. Calculations carried out with dissimilar metals are compared with experiments in terms of fusion zone size and displacements.

PVP2006-ICPVT-11-93155 pp. 81-86; (6 pages)
doi:10.1115/PVP2006-ICPVT-11-93155

In the study of the seismic behaviour of structures, the Soil Structure Interaction (SSI) is concerned with the interaction between the soil, from which come the solicitation, and the structure (building, industrial installation, ...). The SSI can be considered as a kind of multi physic problem. The physical phenomena for the soil or the structure are described by the same equations. But, for the soil, the best point of view is to consider wave’s propagation in an infinite medium, whereas for the structure, the most suitable approach is, in many case, to use eigen modes on the modal basis. The currently used numerical methods for SSI consider two different domains, with interactions at the interface. Boundary Element Methods (BEM) and Finite Element Methods (FEM) can be used. An application is presented, with the interpretation of test performed in Japan, for a Structure Soil Structure Interaction (SSSI) problem, considering the interactions between two adjacent buildings during an earthquake. The tests were performed by JNES in Japan, and the interpretations presented here are performed by CEA, in France, using FEM methods. The field test experiments have been carried out by NUPEC (JNES) under different conditions with one building, two identical buildings or two different buildings in an excavation, for the “surface configuration”, and in the “embedded configuration”, when the excavation is filled. Forced vibration test and earthquake observations are being carried out in the field test. NUPEC proposed a theoretical model for the interpretation of the experimental results, including soil and buildings mechanical characteristics. The results obtained with this model are similar to the experimental ones. Sensibility analyses have been developed, based on the NUPEC theoretical model, for the forced vibration tests and the seismic motion. It is possible to reproduce, with numerical simulations, the fact that, for two buildings, the movement under a seismic solicitation is a little lower for two adjacent buildings than for one isolated building.

Topics: Soil
PVP2006-ICPVT-11-93156 pp. 87-94; (8 pages)
doi:10.1115/PVP2006-ICPVT-11-93156

The considered structure is a nuclear reactor vessel, composed of two concentric inner and outer structures, with water in the annular space between. Previous dynamic analysis showed that this water lead to strong fluid structure interaction coupling the structures. The annular space is filled by regularly spaced cylinders, which are linked to the inner structure. Their influence was neglected in the first studies. Recent analyses, using homogenization methods, show that these cylinders increase the FSI coupling in the vessel. The homogenization methods is based on general principles developed in the study of tube bundles, and very well established, from a physical and numerical point of view. Even if it seems reasonable to have a high degree of confidence in the results obtained with this homogenization methods, it is still interesting to validate the results of the “homogenization analysis” with a comparison with “direct calculations”, taking into account the real geometry of the system. The paper presents the main results of the validation. The main limitation of the “direct calculations” is the size of the mesh and the computer time. The main limitation for the “homogenization analysis” is that the actual modeling does not take into account the anisotropy in the Fluid Structure Interaction in the annular space.

PVP2006-ICPVT-11-93157 pp. 95-104; (10 pages)
doi:10.1115/PVP2006-ICPVT-11-93157

The present paper exposes the main directions of a R&D program that DCN and CEA are currently developing to study the dynamic response of the steam generator of a naval nuclear propulsion reactor submitted to a shock. The structure is composed of tube bundles, immersed in a two phase flow fluid (steam and water). The dynamic solicitation contains high accelerations and high frequencies. It is thus necessary to establish which kind of physical phenomena can take place, and which kind of numerical tool can be used to study the dynamic behavior of the system. If the acceleration and the frequencies are very high, it will be necessary to consider highly non linear physical phenomena, with large deformation within short time duration. If the acceleration and (or) the frequencies are lower, simpler methods can be considered, assuming a linear behavior for the structure. In the latter case, as the frequencies still remain higher than the seismic ones, it might be necessary to take into account different kind of eigenmodes, as those depending on the fluid compressibility. As the fluid is a two phase medium, the use of homogenized fluid model has to be investigated. Since the tube bundle is a periodic structure, a homogenization technique can be used. Basic principles of the method are recalled as well as potential developments of existing methods. Influence of dissipative effects has also to be evaluated. The paper exposes the various problems that have to be addressed in order to produce a physical model of the structure that takes into account the various fluid-structure interaction effects for the shock analysis of the steam generator.

PVP2006-ICPVT-11-93184 pp. 105-114; (10 pages)
doi:10.1115/PVP2006-ICPVT-11-93184

The paper deals with an implicit partitioned solution approach for the numerical simulation of fluid-structure interaction problems. The solution procedure involves the finite-volume flow solver FASTEST, the finite-element structural solver FEAP, and the coupling interface MpCCI. The method is verified and validated by comparisons with benchmark results and experimental data. Investigations concerning the influence of the grid movement technique and an underrelaxation on the performance of the method are presented.

PVP2006-ICPVT-11-93212 pp. 115-121; (7 pages)
doi:10.1115/PVP2006-ICPVT-11-93212

In order to analyze the Fluid-Structure Interaction (FSI) between a flow and a flexible structure, an algorithm was presented to couple the Lattice Boltzmann Method (LBM) and the Finite Element Method (FEM). The LBM was applied to the fluid dynamics while the FEM was applied to the structural dynamics. The two solution techniques were solved in a staggered manner, i.e. one solver after another. Continuity of the velocity and traction was applied at the interface boundaries between the fluid and structural domains. Furthermore, so as to make the fluid-structure interface boundary more flexible in terms of the computational modeling perspective, a technique was also developed for the LBM so that the interface boundary might not coincide with the fluid lattice mesh. Some example problems were presented to demonstrate the developed techniques.

PVP2006-ICPVT-11-93213 pp. 123-135; (13 pages)
doi:10.1115/PVP2006-ICPVT-11-93213

Detonation of high explosive due to impact of fragments and flyer plates was modeled using hydrodynamic computer code. Included in the model were the warhead consisting of casing and high explosive (which is H-6 in this case). An 80-gram fragment simulated projectile (FSP) was used as the projectile. Flyer plates considered are single- and multi-layer structures. A reactive flow model which is able to capture the initiation, propagation and complete detonation or deflagration of detonation was used to predict the occurrence of complete detonation. Analyses were performed with several impact velocities to obtain the velocity beyond which complete detonation would occur. Shields have been used to mitigate mechanical shocks. It has been well established that shields with multi-layered materials with impedance mismatch would reduce shock levels significantly. A numerical study was conducted to derive an optimum shield design with this concept. The model used encompasses a warhead-canister system. It was assumed that one of the two adjacent warheads would detonate. The canister wall was made of multi-layered materials consisting of layers of materials made of metal and lucite. This material combination represents a medium degree of mismatch while still exhibiting certain amount of strength. The model determines the pressure level at explosive in the neighboring warhead. The pressure level was used to determine if detonation would occur, and provided a measure of effectiveness on the shields for shock mitigation.

PVP2006-ICPVT-11-93236 pp. 137-146; (10 pages)
doi:10.1115/PVP2006-ICPVT-11-93236

The feed water nozzle of the steam generator constitutes an area where exists a very high spatial thermal gradient, and also occasionally a temporal thermal gradient, for example during starting of the installation. In order to protect the vessel from thermal fatigue, the cold pipe is surrounded at the connection by an annular water layer to ensure thermal uncoupling. However the flow behavior remains unknown. In a first step, we improve our knowledge concerning the hydraulic behavior thanks to a model representing a simplified geometry of the nozzle environment. In a second step we confirm this behavior thanks to CFD parametric analysis of the geometry. These two first steps allowed us to identify the best geometrical dimensions, such as the depth and the thickness of the annular cavity, but also the curved or sharp junction. These parameters concern the mass transfer in the annular cavity. The current step concerns the thermal effects. The analysis is performed by both experimental and numerical approach. The experimental method to identify heat fluxes is presented, then the results are discussed and compared to numerical results.

PVP2006-ICPVT-11-93239 pp. 147-156; (10 pages)
doi:10.1115/PVP2006-ICPVT-11-93239

During the normal cycle of a pressurized water reactor, boron concentration is reduced in the core until fuel burns up. A stretch out of the normal cycle is however possible afterwards, provided primary coolant temperature is reduced. In those stretch out periods, nuclear operators want to keep constant thermal power exchanged in the steam generator, in order to preserve its performances. Under that constraint, the required reduction in primary coolant temperature involves both a decrease of secondary cooling system pressure and an increase of tube bundle vibrations. Since neither pressure nor vibrations should exceed some given thresholds in order to preserve component integrity, the reduction of primary coolant temperature has to be limited. Nuclear plant operators thereafter need an operating diagram, i.e. a diagram that provides minimum allowed primary coolant temperature versus power rate. In that context, we propose a method to derive such a diagram, by combining, on the one hand a code for simulating primary and secondary fluid flows in steam generators and, on the other hand, a software that allows one to predict fluid elastic tube bundle instabilities. That method allows one to take into account both tube fouling and plugging. It is now used by French utility “Electricité De France”, in order to check or supplement the analysis that are provided by steam generator manufacturers.

PVP2006-ICPVT-11-93258 pp. 157-164; (8 pages)
doi:10.1115/PVP2006-ICPVT-11-93258

The work is developed within the general frame of marine structure design. The study presents a numerical investigation of the hydro elastic behaviour of a deformable lifting body in a uniform steady flow. The fluid is considered as inviscid. The structure problem is solved by a finite element method and the flow problem is solved by a finite volume method using two commercial codes. Both problems are coupled through an iterative algorithm based on the exchange of boundary conditions at the flow-structure interface. The study is conducted on a cambered rectangular hydrofoil mounted in a hydrodynamic tunnel simulating the experiment that is currently performed in our laboratory. Results obtained from the fluid-structure computations including the deformation together with the hydrodynamic coefficients are presented. The influence of the fluid-structure coupling has been highlighted through comparisons with “non-coupled” simulations. Depending on the flow conditions, the twist of the hydrofoil together with the hydrodynamic loading are observed through the coupled simulation.

PVP2006-ICPVT-11-93262 pp. 165-172; (8 pages)
doi:10.1115/PVP2006-ICPVT-11-93262

In glass container manufacturing (e.g. production of glass bottles and jars) an important process step is the blowing of the final product. This process is fast and is characterized by large deformations and the interaction of a hot glass fluid that gets into contact with a colder metal, the mould. The objective of this paper is to create a robust finite element model to be used for industrial purposes that accurately captures the blowing step of glass containers. The model should be able to correctly represent the flow of glass and the energy exchange during the process. For tracking the geometry of the deforming inner and outer interface of glass, level set technique is applied on structured and unstructured fixed mesh. At each time step the coupled problem of flow and energy exchange is solved by the model. Here the flow problem is only solved for the domain enclosed by the mould, whereas in the energy calculations, the mould domain is also taken into account in the computations. For all the calculations the material parameters (like viscosity) are based on the glass position, i.e. the position of the level sets. The velocity distribution, as found from this solution procedure, is then used to update the two level sets by means of solving a convection equation. A re-initialization algorithm is applied after each time step in order to let the level sets re-attain the property of being a signed distance function. The model is validated by several examples focusing on both the overall behavior (such as conservation of mass and energy) and the local behavior of the flow (such as glass-mould contact) and temperature distributions for different mesh size, time step, level set settings and material parameters.

PVP2006-ICPVT-11-93299 pp. 173-182; (10 pages)
doi:10.1115/PVP2006-ICPVT-11-93299

The internal core baffle structure of a PWR consists in baffles and formers attached to the barrel. Each baffle being independent, the connection between the core baffle sheets, the formers and the core barrel is done thanks to a large number of bolts (about 1500). After inspection, some baffle bolts have been found cracked. This behaviour is attributed to Irradiation Assisted Stress Corrosion Cracking (IASCC). In order to compute accurately the temperature distribution affecting these bolts, EDF has set up a research program. Due to symmetry reasons, only a 45° sector has been accounted for. The three-dimensionnal neutron flux and the gamma induced internal heating are calculated with a Monte-Carlo particle transport code named Tripoli-4. The by-pass flow inside the cavities is computed with the CFD code Code_Saturne with a finite volume technique. Finally, the temperature distribution inside the structure (including all bolts which leads to a considerable solid mesh size — about 236 millions tetraedra) is computed by the thermal code Syrthes using a finite element approach, taking into account both the heating due to the gamma heating deposit and the cooling by the by-pass flow. Calculations show that the solid thermal field obtained exhibit strong temperature gradients and high temperature levels but in very limited zones located inside the material. As expected mainly very limited regions located inside the material and near the corner close to the reactor center are exposed to high temperature levels. On the other hand, calculations clearly confirm that external bolts thightening the core barrel and the formers see temperature much lower than those thightening the baffles.

PVP2006-ICPVT-11-93322 pp. 183-188; (6 pages)
doi:10.1115/PVP2006-ICPVT-11-93322

The pressures of modern competition swimming has increased the desire for the use of technology and science in the pursuit of a speed advantage. This has lead to revolutionary new suits and other equipment such as goggles and for training. Attention to technique and minimising drag have had a less prominent profile but are beginning to become more important. Part of the lack of advancement has been that a swimming stroke is very complex action and determining precise angles and orientations is necessary before drag and lift calculations can be undertaken. Work has been done that has established that the hand could be treated as an aerofoil. Work was undertaken to numerically model a mechanical hand that was being used to undertake both static and dynamic experimental testing within a flume. This paper is concerned with the initial modelling phase and static testing. It will look at comparisons of data at different incident angles and different flow velocities to establish the validity of progressing this work. Issues with the generic nature of the model will also be addressed.

Topics: Modeling , Water
PVP2006-ICPVT-11-93340 pp. 189-194; (6 pages)
doi:10.1115/PVP2006-ICPVT-11-93340

In this study, the destruction of concrete block using underwater shock wave generated by electric discharge was studied. Initially, the shock wave generated by electric discharge was investigated by optical observation using a high-speed camera and pressure measurement. A comparison of the underwater shock wave generated from the electrode with and without connecting a metal wire was made. A metal wire was connected to an electrode and a high voltage impulsive current was passed through it to generate the underwater shock wave. A hole was made in the concrete block, filled with water and an electrode was inserted into the hole, which acts as a pressure vessel. The electric current was passed through this electrode to generate underwater shock wave for the destruction of concrete block.

PVP2006-ICPVT-11-93347 pp. 195-200; (6 pages)
doi:10.1115/PVP2006-ICPVT-11-93347

In order to consolidate metal powders, the present investigation uses a shock wave derived from the detonation of an explosive and it’s called a shock compaction method. In the present investigation, we employed an ultra-high pressure generation device in order to generate underwater shock wave. The underwater shock wave is derived from the detonation wave in a water container and after that underwater shock wave is converged in the central axis. Finally, the high pressure of underwater shock wave is uniformly impinged on the powders. In case of experimental data that is measured by manganin gauge, the peak pressure of underwater shock wave is 16.8GPa, the result of numerical analysis is 17.9GPa. Considering for the measurement error (1GPa), it seems to be good agreement between the result of numerical analysis and experiment. Nd-Fe-B magnetic material powders are tried to consolidate using the assembly under optional temperatures by heating system and the samples recovered under different conditions were examined in terms of magnetic properties.

PVP2006-ICPVT-11-93348 pp. 201-210; (10 pages)
doi:10.1115/PVP2006-ICPVT-11-93348

Defects are commonly in weld joints depending on the process condition and workmanship of the welding process. Under good control environment, the amount and size of the defects can be very small and do not compromise the integrity of the weld joints. In other cases, the amount and size of the defects in the weld joints can be large and, therefore, can limit the integrity of the structure. Determination of critical flaw sizes of the welds requires accurate calculation of stress intensity factors of cracks of various lengths at different locations for their use in crack growth evaluation under cyclic loading. Two commonly used welded joints, namely butt and corner weld joints, were investigated. Three crack configurations for each of the two welded joints were considered. Finite element method was used in conjunction of the M-integral to obtain the stress intensity factors for various lengths of the cracks. Results were then used to perform the fitness-for-purpose assessment of these welds under spectral loading. Methodology and results of the stress intensity factor calculation for the above-mentioned cracks are covered in this paper.

PVP2006-ICPVT-11-93349 pp. 211-216; (6 pages)
doi:10.1115/PVP2006-ICPVT-11-93349

There are a lot of studies related to the shock wave which generated by explosive, for example, explosive compaction, explosive cladding, and explosive forming. It is necessary and indispensable in these studies to know the material characteristics of container loaded with an explosive. Since the force of a shock wave changes with the material of containers. To investigate the material characteristics of a container, the shock wave propagating in the material has analyzed. In this research, Polymethylmethacrylate (PMMA) which usually used as loading container of explosive used as container material. For analysis, the pressure measurement experiment by the manganin gauge (Kyowa Electric Industrial Co., ltd.,), numerical analysis by LS-DYNA3D (commercial program based on the explicit finite element code) and optical observation by high-speed are used. A lot of data about the shock wave propagating in PMMA was obtained.

Topics: Shock waves
PVP2006-ICPVT-11-93353 pp. 217-221; (5 pages)
doi:10.1115/PVP2006-ICPVT-11-93353

In this report, we propose a new explosive welding method, and the welding is performed at employing underwater shock pressure produced by the underwater explosion of an explosive placed at one side almost vertical to the specimen to be welded. In order to prevent the reduction of the shock pressure with the distance away from explosive, a steel reflector is placed over the area of the specimen. The effects of the reflector are investigated based on the experimental results and the process is numerically analyzed results.

PVP2006-ICPVT-11-93354 pp. 223-231; (9 pages)
doi:10.1115/PVP2006-ICPVT-11-93354

The paper presents the progress in the development of a novel unified method for solving coupled fluid-structure interaction problems as well as the associated major challenges. The new approach is based on the fact that there are four fundamental equations in continuum mechanics: the continuity equation and the three momentum equations that describe Newton’s second law in three directions. These equations are valid for fluids and solids, the difference being in the constitutive relations that provide the internal stresses in the momentum equations: in solids the stress tensor is a function of the strain tensor while in fluids the viscous stress tensor depends on the rate of strain tensor. The equations are written in such a way that both media have the same unknown variables, namely the three velocity components and pressure. The same discretisation technique (finite volume) and solution method (segregated approach) are used irrespective of the medium. Also the same methodology to handle the pressure-velocity coupling is employed. A common set of variables as well as a unified discretisation and solution method leads to a strong coupling between the two media and is very beneficial for the robustness of the algorithm. Significant challenges include the derivation of consistent boundary conditions for the pressure equation in boundaries with prescribed traction as well as the handling of discontinuity of pressure at the fluid-structure interface.

PVP2006-ICPVT-11-93356 pp. 233-240; (8 pages)
doi:10.1115/PVP2006-ICPVT-11-93356

The explosive forming is one of the forming methods of metal plates has been performed since 1950. This method is different from usual static press forming. The metal plate is accelerated by underwater shock wave, which is generated by underwater explosion of an explosive. We have tried the experiment of aluminum alloy forming using this method. In this research, a forming limit for aluminum alloy has been clarified from the experimental results. Then, we have tried the numerical simulation for this method using finite difference method. In this research, two methods for forming aluminum plates using closed metal vessel and paper vessel are introduced and the results of numerical simulations corresponding to those experimental conditions are shown.

Topics: Alloys , Explosives
PVP2006-ICPVT-11-93367 pp. 241-250; (10 pages)
doi:10.1115/PVP2006-ICPVT-11-93367

Based on LEAT’s discrete element codes, granular flow and mixing on conveying equipment is studied in two and three dimensions. Discrete element simulations, which are briefly introduced, provide detailed information on particle positions and velocities over time. This information is used to derive quantities characterizing the dynamic process of mixing. The main focus of the study presented is the mixing process of inhomogeneous particle ensembles on different grate types. For this purpose the introduced mixing parameters are used to compare the mixing in a 3D situation with the corresponding 2D approximation on identical grates and to compare different grate designs in two dimensions.

PVP2006-ICPVT-11-93379 pp. 251-256; (6 pages)
doi:10.1115/PVP2006-ICPVT-11-93379

The effect of shear thinning on the stability of the Taylor-Couette flow (TCF) is explored for a Carreau-Bird fluid in the narrow-gap limit to simulate journal bearings in general. Also considered is the changing eccentricity to cover a wide range of applied situations such as bearings and even articulation of human joints. Here, a low-order dynamical system is obtained from the conservation of mass and momentum equations. In comparison with the Newtonian system, the present equations include additional nonlinear coupling in the velocity components through the viscosity. It is found that the critical Taylor number, corresponding to the loss of stability of the base (Couette) flow becomes lower s the shear-thinning effect increases. Similar to Newtonian fluids, there is an exchange of stability between the Couette and Taylor vortex flows. However, unlike the Newtonian model, the Taylor vortex cellular structure loses its stability in turn as the Taylor number reaches a critical value. At this point, A Hopf bifurcation emerges, which exists only for shear-thinning fluids. Variation of stresses in the narrow gap has been evaluated with significant applications in the non-Newtonian lubricant.

PVP2006-ICPVT-11-93382 pp. 257-261; (5 pages)
doi:10.1115/PVP2006-ICPVT-11-93382

Nowadays, the simulation of forming processes is rather well integrated in the industrial numerical codes. However, to take into account the possible modifications of the tool during cycle of working, we develop dedicated numerical software. This one more particularly will allow the identification of the fatigue criteria of the tool. With the view to conceiving the optimal shapes of tool allowing increasing their lifespan while ensuring a quality required of the part thus manufactured. This latter uses coupling with friction finite element method — for modelling the axi-symmetric part — and boundary element method — for modelling the tool. For the validation, we modeled forming process.

PVP2006-ICPVT-11-93383 pp. 263-268; (6 pages)
doi:10.1115/PVP2006-ICPVT-11-93383

Various liquids are commonly transported through metal pipes. For reasons of safety it is important to understand the behavior of pipes when subject to an explosive loading from within. This research paper is concerned with examining the expansion and destruction of metal pipes subjected to a high power explosion by high explosive. An experimental study was carried out for this research and visualized using high-speed camera images. Results were then compared to a computer simulation of the same problem. Numerical simulations are performed in three dimensions using the LS-DYNA code. Results obtained numerically compared well to those from experiment.

Topics: Metals , Pipes , Explosives
PVP2006-ICPVT-11-93386 pp. 269-276; (8 pages)
doi:10.1115/PVP2006-ICPVT-11-93386

The essential features for an adequate simulation of water hammer effects are incorporated in the one-dimensional fluiddynamic code ROLAST. This code was developed for the calculation of transient load cases in piping networks, including active and passive components like pumps, valves, check valves, vessels, and allowing for various boundary and initial conditions. The essential models for water hammer treatment are described like condensation, air bubble behaviour and venting, and especially their adaptation to the 1D flow formulation. Examples of validation are given. The role of dissolved air is discussed. The effects of dynamic friction and coupling with the structural analysis on a realistic damping behavior are explained. The code allows the calculation of realistic water hammer loads on the system by considering the reaction of components like check valves at the some time.

PVP2006-ICPVT-11-93387 pp. 277-284; (8 pages)
doi:10.1115/PVP2006-ICPVT-11-93387

In piping design hydraulic load cases and the resulting dynamic structural loads are induced and generated by strongly time dependent pressure surges and subsequent oscillations. Therefore, with liquid filled piping, the implementation of fluid-structure interaction by coupling the fluiddynamic and the structural dynamic codes gives a substantial contribution to more realistic loading results. Considering this effect, usually a load reduction due to energy losses and the phase and frequency shift from fluid to structure and vice versa is achieved. In cases of fluid structure resonance the results are more reliable and can help to develop an optimized support concept. To realize the coupled calculation of both codes they are bundled by a special user environment, where the coupling points are specified and marked. We describe the input of fluid forces at those points and the treatment of the liquid masses inside the piping, as well as the method of back-coupling the resulting structural displacements into the fluid calculation. The method was validated against measurements of load cases in power plant piping systems and experimental results for various boundary conditions. The most realistic results were obtained by combining the coupling with the application of dynamic friction in the fluid code.

PVP2006-ICPVT-11-93430 pp. 285-290; (6 pages)
doi:10.1115/PVP2006-ICPVT-11-93430

A newly developed approach for tridimensional fluid-structure interaction with a deformable thin porous media is presented under the framework of the LS-DYNA software. The method presented couples a Arbitrary Lagrange Euler formulation for the fluid dynamics and a updated Lagrangian finite element formulation for the thin porous medium dynamics. The interaction between the fluid and porous medium are handled by a Euler-Lagrange coupling, for which the fluid and structure meshes are superimposed without matching. The coupling force is computed with an anisotropic Ergun porous flow model. As test case, the method is applied to an anchored porous MIL-c-7020 type III fabric placed in an air stream.

PVP2006-ICPVT-11-93433 pp. 291-296; (6 pages)
doi:10.1115/PVP2006-ICPVT-11-93433

In recent years, the use of cryogenic fluids as a coolant has been increasing because of the industrial development of low temperature technology. Therefore, the use of the cryogenic pressure vessel and piping become general. LNG-tank, LN2 , O2 -tank at food factory and medical facilities are given for example. The safety of these pressure containers becomes important all the more. Thermal insulation of these cryogenic vessel and piping is usually carried out by using evacuation. In the cryogenic pressure vessel and piping, reducing the thermal insulation of that by initial small damage, leads to an internal pressure rise and occurring of flashing, and causing secondary crush of pressure vessel and piping also. Then, we conducted experiments with shock loading of commercial tanks and numerical simulation of shock loaded the double wall that contain vacuum layer. When thinking about safety aspects, it is important to consider about the spread of the shock wave in the double wall containing the vacuum layer.

PVP2006-ICPVT-11-93441 pp. 297-302; (6 pages)
doi:10.1115/PVP2006-ICPVT-11-93441

Fracture control in blasting is very important in underground excavation and demolition of concrete structures. It is valuable to obtain an understanding of the dynamic behavior of stress waves in the blasting process for the development of fracture control method. Experimental visualizations and numerical simulations were performed to observe the propagation and interaction of stress waves between two charge holes in blasting. These are related with control of fracture planes along the line connecting the charge holes in smooth blasting. In model experiments using PMMA plates, the stress waves were generated by initiation of electric detonators at the charge holes and were observed by means of the visualization system. The dynamic behavior of stress waves in the blasting process was also visualized by numerical simulation using the smoothed particle hydrodynamics (SPH) method. The dynamic behavior of stress waves is discussed by means of the experimental results and the simulation results.

Topics: Stress , Waves
PVP2006-ICPVT-11-93443 pp. 303-308; (6 pages)
doi:10.1115/PVP2006-ICPVT-11-93443

The establishment of the sterilization technology in non-heating environment is requested in the food industry and a lot of other fields. The existing sterilization technology using the high pressure is mainly liberating rapid pressure and a lot of loadings. In this research, the sterilization by a high pressure was tried by using the underwater shock wave caused by explosive. The detonating fuse was detonated with the percussion cap, and the shock wave was generated. Bacillus cereus, Escherichia coli, Pseudomonas aeruginosa, Staphylococcus aureus, Saccharomyces cerevisiae were used. The underwater shock wave barely causes heat. An excellent bactericidal effect of 100% was obtained in the maximum in the experiment that used S. cerevisiae.

PVP2006-ICPVT-11-93446 pp. 309-312; (4 pages)
doi:10.1115/PVP2006-ICPVT-11-93446

The Boundary Element Method is one of the most used techniques for the simulation of acoustic problems especially for external ones. However, it leads to large computational time because of the complex character of the resulting linear system and the calculation of its different terms by surface integration. In this paper, the Rayleigh method is used to calculate the acoustical pressure at any point in the space. This method is very fast since it does not need to construct and to solve a linear system.

Topics: Acoustics , Simulation
PVP2006-ICPVT-11-93462 pp. 313-318; (6 pages)
doi:10.1115/PVP2006-ICPVT-11-93462

In the food industry, it is hoping high value-aided product and the increase in efficiency of food processing. On the other hand, we get an experimental result that the load of the shock wave improves an extraction of food, and soften food. But, the safe and high efficiency pressure vessel for the processing is necessary to apply these technologies to the food processing field actually. Therefore, we are planning the development of the pressure vessel for food processing. The fundamental data of the shock loading to food are necessary in order to make suitable vessel. As for these data, it is variety the specifications required by the kind of food and effect to expect. We report the result that shock wave loading was done to various food.

PVP2006-ICPVT-11-93470 pp. 319-324; (6 pages)
doi:10.1115/PVP2006-ICPVT-11-93470

In this study, it has aimed at the design of the pressure vessel where an underwater shock wave is applied to food efficiently. This study aims at the desigh of a pressure vessel in which the underwater shock wave generated by the underwater explosion of detonating fuse was experimentally investigated by the optical observation and the pressure measurement. Therefore the pressure vessel is designed so that suitable pressure may apply on food. This designed vessel is evaluated by the numerical analysis that used LS-DYNA3D. The interaction of the underwater shock wave, the incident wave and the reflected wave are investigated by the numerical analysis. The agreement between the experimental results and the numerical analysis was found to be good.

PVP2006-ICPVT-11-93477 pp. 325-330; (6 pages)
doi:10.1115/PVP2006-ICPVT-11-93477

A new attempt in developing a composite material using explosive processing was attempted. Shock wave derived from explosion energy is a viable technique and can be used to penetrate diamond powders into the metal pipe without permitting the reaction with the base metal. In this method, the overall heat conductivity property of the composite is expected to be improved by the diamond powders, which possess high heat conductivity property. The purpose of this research is to clarify the experimental conditions for obtaining a new composite material with unique properties. Some sizes powders were used for the experiments and the difference in the experimental results are reported.

PVP2006-ICPVT-11-93478 pp. 331-334; (4 pages)
doi:10.1115/PVP2006-ICPVT-11-93478

Supercritical fluid is the fluid in the state where the limit (critical point) of temperature pressure that a liquid and gas coexist was exceeded. This is a fluid to which it has a big kinetic energy similar to the gas molecule, and the high molecular density that equals a liquid has it. In fact, supercritical fluid has dissolution power like a liquid, and has diffusivity like a gas. Therefore, supercritical fluid has a possibility of becoming the ideal solvent. The experiment purpose is a resolution of the organism by the supercritical reaction. We designed the supercritical reaction container with which both of the fluid, water and carbon dioxide, can correspond. Supercritical demanded the severe resisting pressure, heatproof, and resistance to corrosion with the container. A supercritical temperature of water is 374.1°C, and supercritical pressure is 22.06 MPa. IT was designed in consideration of the safety rate to resist the temperature of 500°C and the pressure of 50MPa. We designed the container of the batch type with comparatively easy structure, and made of the stainless steel and the amount of the contents is 375ml. Next, the condition of the heating furnace is described. Power consumption is 1500W, and the maximum temperature is 600°C. Supercritical state is controlled at the temperature. Heating it raises the pressure in the container and it reaches a supercritical temperature and supercritical pressure. Finally in the experiment, it was confirmed to endure even 25MPa.

Topics: Containers
PVP2006-ICPVT-11-93482 pp. 335-340; (6 pages)
doi:10.1115/PVP2006-ICPVT-11-93482

Underwater shockwave is easily generated by means of explosion of explosive and by means of high voltage electric discharges in water. It has characteristics of high pressure, very short duration of action, and permeation [1]. Therefore, underwater shockwave can destroy only materials inside without destroying their outside. We tried using application of underwater shockwave to some foods as food processing device. At this experiment, foods were applied underwater shockwave by using detonating fuse and electric detonator in water tank. Foods sample was apples, Japanese radishes, and burdocks. In the result, foods were made soft. From result of apples, we easily got juice by squeezing by woman’s power without grating up apples. And there was difference of content of polyphenols in juice between application underwater shockwave to apples and non-application. Extraction of Japanese radish was improved. From these experimental results, we suggest necessity spec of shockwave processing vessel for food processing.

PVP2006-ICPVT-11-93483 pp. 341-346; (6 pages)
doi:10.1115/PVP2006-ICPVT-11-93483

We tried hot explosive compaction to make bulk materials of hard-to-consolidate powders using cylindrical configuration. By heating above 1000°C, it is possible to give the ability of plastic deformation for hard ceramic powders and also possible to enhance the surface melting to bond each particle. Using the cylindrical configuration, hot explosive compaction experiment was carried out for consolidation of TiB2 powders at elevated temperature. A central hole and a melting spot at the end of the tube were observed for a sample recovered. High compaction density and high hardness (above 3000 VHN highest) were measured for the samples recovered. The central hole and the melting spot are considered to be generated by the formation of mach stem at the center and the high-velocity collision towards the end plug. Numerical simulation was carried out using AUTODYN-2D code and compared with the experimental results for the TiB2 compacts.

PVP2006-ICPVT-11-93551 pp. 347-350; (4 pages)
doi:10.1115/PVP2006-ICPVT-11-93551

The main concern in fluid-structure interaction problems is the computation of fluid forces that act on a rigid or deformable structure. However, the majority of numerical test consists in employing two different codes to separately solve pressure of the fluid and structural displacements. In this paper, a monolithic with an ALE formulation approach is used to implicitly calculate the pressure of an incompressible fluid applied to the structure. The velocity-pressure formulation is decoupled by the projection method proposed by Gresho.

PVP2006-ICPVT-11-93555 pp. 351-355; (5 pages)
doi:10.1115/PVP2006-ICPVT-11-93555

The deployment of an airbag is most fatal and dangerous to a passenger when they are in an out of position (OOP) situation, with the airbag making contact before it is fully inflated. This can lead to severe, if not life threatening, injuries to the passenger. This situation is more commonly associated with small females and children who are positioned near to the airbag module, i.e. in an OOP load cases. The aim of this research is to assess the response of a Hybrid III 5th Percentile female anthropomorphic dummy positioned in a FMVSS 208 low risk static airbag deployment OOP load cases using a transient dynamic finite element program called LS-DYNA. The simulation considers the standard procedures utilised in the LS-DYNA, where assumptions such as uniform airbag pressure and temperature are made, along with a more recently developed procedure that takes into account the fluid-structure interaction between the inflating gas source and the airbag fabric, referred to as Arbitrary Lagrangain Eulerian (ALE) theory. Both simulations were compared to test data received by Jaguar, indicating satisfactory results in terms of correlation, with the more recently developed procedure, ALE theory, showing the greatest accuracy, both in terms of graphical and schematic comparison, especially in the very early stages of the inflation process. As a result, the new simulation procedure model was utilised to research into the effects of changing the designs of the airbag module.

Topics: Simulation , Stress , Airbags
PVP2006-ICPVT-11-93557 pp. 357-361; (5 pages)
doi:10.1115/PVP2006-ICPVT-11-93557

In recent years there have been numerous attempts to accurately model phenomena that occur in the cardiovascular system of the human body. Problems of the cardiovascular system are commonly associated with low survival rates, thus attracting great interest. One specific area of concern are mechanisms by which the aorta suffers heavy damage during automotive impacts. A large number of fatalities could be prevented annually with the design of new safety systems arising from a proper understanding of these mechanisms. It is well known that such injuries are a result of complex interactions between the vessels, the blood they carry and other parts of the body. As such they can only be accurately modelled using advanced multi-physics software. This research examines a number of material models for use in aortic impact problems and aspires towards the development of a layered orthotropic blood vessel model.

Topics: Modeling , Aorta
PVP2006-ICPVT-11-93670 pp. 363-380; (18 pages)
doi:10.1115/PVP2006-ICPVT-11-93670

Detonation waves in gas-filled piping or tubing pose special challenges in analysis and prediction of structural response. The challenges arise due the nature of the detonation process and the role of fluid-structure interaction in determining the propagation and arrest of fractures. Over the past ten years, our laboratory has been engaged in studying this problem and developing methodologies for estimating structural response. A brief overview of detonation waves and some key issues relevant to structural waves is presented first. This is followed by a summary of our work on the elastic response of tubes and pipes to ideal detonation loading, highlighting the importance of detonation wave speed in determining flexural wave excitation and possibility of resonant response leading to large deformations. Some issues in measurement technique and validation testing are then presented. The importance of wave reflection from bends, valves and dead ends is discussed, as well as the differences between detonation, shock wave, and uniform internal pressure loading. Following this, we summarize our experimental findings on the fracture threshold of thin-walled tubes with pre-existing flaws. A particularly important issue for hazard analysis is the estimation of loads associated with flame acceleration and deflagration-to-detonation transition. We give some recent results on pressure and elastic strain measurements in the transition regime for a thick-wall piping, and some remarks about plastic deformation.

Topics: Explosions , Pipes
PVP2006-ICPVT-11-93701 pp. 381-388; (8 pages)
doi:10.1115/PVP2006-ICPVT-11-93701

The surround and the spider of the loudspeaker suspension are modelled in ANSYS to carry out finite element analysis. The displacement dependent nonlinearities arising from the suspension are studied and the material and geometric effects leading to the nonlinearities are parameterised. The ANSYS models are simulated to be excited by a sinusoidal load and the results are evaluated by comparison with the results obtained by a physical model. The paper illustrates how practical models can be analysed using cost effective finite element models and also the extension of the models to experiment on various parameters, like changing the geometry for optimisation, by computer simulation.

PVP2006-ICPVT-11-93717 pp. 389-394; (6 pages)
doi:10.1115/PVP2006-ICPVT-11-93717

The present work is devoted to simulation of fluid-structure interaction and flow-induced vibration problems by using a partitioned procedure. A finite element structure solver is coupled with a finite volume fluid solver. A coupling interface has been developed for grid interpolation and scheme coupling control. An alternative mesh motion to a classical ALE formulation is proposed for the fluid computation and the method is validated by means of a test-case involving a pipe conveying fluid.

PVP2006-ICPVT-11-93861 pp. 395-399; (5 pages)
doi:10.1115/PVP2006-ICPVT-11-93861

Acoustic materials are used to treat indoor and outdoor spaces to make speech intelligible, and places less noisy and more pleasant to be in. Whilst most treatments are old and well established, in recent years there has been a growth in innovative products, which overcome difficulties with the old technologies, especially when making the treatments more visually acceptable to architects. Modern construction depends a great deal on acoustic materials to act as sound containment or sound control, either in residential or commercial applications. Sound-absorbing materials are highly porous to increase their sound absorption qualities. The amount of absorption depends on the thickness of the porous material, the size and number of pores, and the frequency of the noise. When painting acoustic materials, the painter should be very careful that the paint does not close up the acoustic surfaces; perforations or fissures. It is through these openings in the surface that sound waves enter the body of the acoustic material and are absorbed. It is the control of the paint droplet size upon the surface that affects the acoustic properties and the aesthetic appearance of the coated surface. An investigation into the coating performance with regard to acoustic absorption and aesthetic appearance was performed in a true-scale automotive spray booth using five different types of paint: three aerosol paints, domestic emulsion and acoustic paint. The sprays produced by the aerosols, emulsion and acoustic paints, applied using an air assist spray-gun, were characterised using a Mastersizer-X laser instrument. The flow rate of the paint through the spray gun was varied during the experiments between 50 ml/min and 500 ml/min. The work has highlighted the operating parameters for the air-assist spray gun in order to produce the smallest drop sizes. The measuring of the acoustic coefficient of the coated materials has shown that the aerosol and air-assist gun produced too large a droplet to produce a good acoustic coating. The use of the acoustic paint did create a good absorption coefficient but the work has highlighted the requirement for the atomizing process to be optimised for this highly viscous acoustic paint.

PVP2006-ICPVT-11-93862 pp. 401-409; (9 pages)
doi:10.1115/PVP2006-ICPVT-11-93862

The unsteady flow through normal triangular tube arrays is simulated applying the Cloud-in-Element method. The scheme realizes time-stepping via a Langrangian vortex method using random-walk to model diffusion in the flow. The vortex particle velocities are computed on a fixed unstructured grid at each time step. Zero normal velocity on solid boundaries is enforced by a source panel method and zero slip is achieved by introducing vorticity into the flow at each time step. Simulations have been carried out for normal triangular tube arryas with pitch ratios of 1.32, 1.61, 2.08, 2.63 at Reynolds numbers of 1000, 3000, 5000 and 10000. Single vortex shedding frequencies have been observed for the smaller pitch ratios while two Strouhal numbers are obtained for the sparse arrays. This is consistent with experimental data in the literature. Also the overall flow structures were captured successfully.

PVP2006-ICPVT-11-93963 pp. 411-418; (8 pages)
doi:10.1115/PVP2006-ICPVT-11-93963

Buildings located in industrial gas production areas are normally designed to withstand explosion pressures from a design accidental event in the plant. To protect personnel and equipment inside buildings, installation of shock valves is the normal procedure. Experience with shock valves is, however, that they require maintenance, are expensive, have corrosion problems, and add pressure losses in the ventilation system. Alternatives are to reinforce fire and gas dampers in areas where shock pressures are moderate. Design pressures and possible effects of damping chambers and location of dampers are important variables. The paper summarizes some of the main results and conclusions provided from a study done for the Norwegian company Hydro Oil & Energy. The main conclusions drawn are as follows: Fortification shock waves have normally significantly shorter durance compared to explosion pressures from a typical accident in a gas process plant, and fortification design guidelines should not be used directly. Dampers should be designed to withstand pressures 1.5–1.8 times the side-on shock pressures unless the dampers are mounted flush with the building wall or roof, due to the reflecting shock pressure from a closed damper mounted inside a ventilation duct.

PVP2006-ICPVT-11-94017 pp. 419-423; (5 pages)
doi:10.1115/PVP2006-ICPVT-11-94017

Currently, a joint effort is made by German research groups to establish a benchmark for a bidirectional Fluid-Structure-Interaction problem: a geometrically non-linear vibrating structure being agitated by a laminar flow of an incompressible Newtonian fluid. Among other approaches, a partitioned solution procedure has been developed in this framework using a high order FEM code for the structural side of the solution coupled to a Lattice-Boltzmann solver discretizing the fluid. The explicit coupling of these two completely different types of discretizations gives promising results also in terms of an efficient calculation. This paper briefly introduces the benchmark, presents the procedure used and gives some results obtained by the application of the method.

PVP2006-ICPVT-11-93280 pp. 1407-1415; (9 pages)
doi:10.1115/PVP2006-ICPVT-11-93280

The 2003 Tokachi-oki earthquake caused the severe damage to oil storage tanks by liquid sloshing. Especially at Tomakomai in Hokkaido, the ground motions at the periods of 3 to 8 sec predominated, which were harmonized with the natural period of liquid sloshing of oil storage tanks, then seven single-deck-type floating roofs were damaged and sank. For the 30,000kl FRT(φ 42.7m), one of those tanks, with about 7 see of fundamental sloshing period, maximum sloshing wave height was estimated 3m and over. On the other hand, for the 100,000kl FRT(φ 78.2m) with about 12 sec of fundamental sloshing period, maximum sloshing wave height was estimated about 1.5m and the excitation of 2nd sloshing mode was considered to be strongly excited. Considering both of nonlinear behavior of a large amplitude wave of 1st sloshing mode and nonlinear effects of large deflection of a deck plate at 2nd sloshing mode, we established the simplified method of seismic design of single-deck-type floating roofs using modified velocity response spectrum. This spectrum was based on many studies, investigated by Zama [1] and others, of the prediction of long-period strong ground motion and of liquid sloshing of oil tanks in Japan.

PVP2006-ICPVT-11-93511 pp. 1417-1425; (9 pages)
doi:10.1115/PVP2006-ICPVT-11-93511

A variational formulation is developed for calculating liquid sloshing effects on the dynamic response of spherical containers under external dynamic excitation. The velocity potential is expressed in a series form, where each term is the product of a time function and the associated spatial function. Because of the configuration of the containers, the associated spatial functions are non-orthogonal, and the problem is not separable and results in a system of coupled non-homogeneous ordinary linear differential equations, which is solved numerically. The solution can be obtained through either direct integration or modal analysis. Sloshing frequencies and masses are calculated rigorously for arbitrary liquid height, and convergence of the solution is thoroughly examined. Particular emphasis is given on the cases of half-full spheres, where explicit expressions for the coefficients of the governing equations are derived. Furthermore, the behavior of nearly-full and nearly-empty vessels is briefly discussed.

PVP2006-ICPVT-11-93531 pp. 1427-1436; (10 pages)
doi:10.1115/PVP2006-ICPVT-11-93531

An analytical solution is presented to predict the sloshing response of a cylindrical liquid storage tank with a floating roof under seismic excitation. The contained liquid is assumed to be inviscid, incompressible and irrotational, while the floating roof is idealized as an isotropic elastic plate with uniform stiffness and mass. The dynamic interaction between the floating roof and the liquid is taken into account exactly within the framework of linear potential theory. By expanding the response of the floating roof into free vibration modes in air and employing the Fourier-Bessel expansion method in cylindrical coordinates, the solution is obtained in an explicit form which is useful for parametric understanding of the sloshing behavior and preliminary study in the early design stage. Numerical results are also provided to investigate the effect of the stiffness and mass of the floating roof on the sloshing response.

PVP2006-ICPVT-11-93622 pp. 1437-1446; (10 pages)
doi:10.1115/PVP2006-ICPVT-11-93622

During the 2003 Tokachi-oki, Japan earthquake, many oil tanks located in Tomakomai were damaged by sloshing due to the long-period strong ground motion. It is especially noted that the single-deck floating-roofs of seven tanks collapsed as they sank with the buckling failure of the pontoons, which resulted in fire accidents of two tanks. To clarify the cause of such damages, it is necessary to investigate in detail the sloshing behaviors in consideration of the existence of a floating-roof. However, so far most of the researches on sloshing have treated only the case of a free surface or the case of a rigid floating-roof, and have not considered the case of an elastic floating-roof, which is used in an actual tank. In this paper, the authors discuss the problem on the basis of fluid-elastic vibration analysis, that is, they investigate the sloshing behaviors of actual floating-roof models with single-deck type and double-deck type and indicate several important viewpoints on the seismic design which has hardly been taken into account hitherto.

PVP2006-ICPVT-11-93750 pp. 1447-1455; (9 pages)
doi:10.1115/PVP2006-ICPVT-11-93750

Nonlinear random interaction of an elastic structure carrying a container, partially filled with liquid, under horizontal narrowband random excitation is investigated. The modal equations of motion are derived by using Galerkin’s method, taking into account the nonlinearity of the hydrodynamic force when the natural frequency of the structure is close to the natural frequency of liquid sloshing. The system response statistics are numerically estimated using Monte Carlo simulation. The influences of the excitation center frequency, its bandwidth and liquid level on the system response are studied. As a result, it is found that the mean square response of the structure decreases as the center frequency approaches to the natural frequency of the structure, and that the sloshing in the container has an effect on the vibration suppression of the structure response.

PVP2006-ICPVT-11-93880 pp. 1457-1467; (11 pages)
doi:10.1115/PVP2006-ICPVT-11-93880

Stability of the steady flow of a viscous liquid through the thick-walled multilayered viscoelastic tubes with different rheological properties of the layers for no stress boundary conditions at the outer surface of the tube is investigated. The eigen values of the system are found. The influence of the material parameters of the layers and the Reynolds number on the spatial and temporal amplification rate of the most unstable mode is investigated. It is shown that the system can be stabilized by increasing the shear modules of the inner and middle layers. The temporal amplification rate significantly decreases and becomes negative with increasing the shear modules of the outer layer, that corresponds to temporal stability of the system. The comparative study of the obtained dependences with the solution of the same problem at no displacement boundary conditions is carried out. The results may be applied to the fluid flows in the ducts of different technical devices as well as to the blood flow in the arteries and veins which are composed of three layers with different functions, structure and material parameters.

PVP2006-ICPVT-11-93920 pp. 1469-1475; (7 pages)
doi:10.1115/PVP2006-ICPVT-11-93920

We investigate the impact of different boundary conditions on the flow field developing around a tilted rectangular cylinder. We are mainly interested in analyzing the changes in force coefficients and in the vortex shedding Strouhal number due to the proximity of the cylinder to a bottom plate (placed at various distances from the cylinder) at different angles of attack. The angle of attack ranges between −30° and +30° and the cylinder elevation above the bottom wall is varied between almost zero and 200 mm. The effects of the different boundary conditions on the vortex shedding phenomenon are investigated by considering the Strouhal number of the vortex shedding as the key controlling parameter. The experimental results mimicking the unbounded conditions (relative large elevation of the cylinder above the solid wall) are in close agreement with those already found in literature. On the contrary, remarkable differences occur when the elevation of the cylinder is decreased. A large body of experimental results is related to the small elevation conditions at different attack angles, where the presence of the wall has a non-negligible effect on the behavior of the force coefficients and Strouhal number of the vortex shedding.

Topics: Fluids , Cylinders
PVP2006-ICPVT-11-93067 pp. 1479-1484; (6 pages)
doi:10.1115/PVP2006-ICPVT-11-93067

Explosion containment vessels (ECVs) are used to fully contain the effects of high explosions. As monobloc thick-walled ECVs, which are widely used now, become larger and thicker, they are difficult in fabrication, high in cost, and uncertain in quality of very thick steel plates. A multilayered ECV (MECV) is presented to develop large-sized ECVs in this paper, which is convenient and economical in fabrication. Under static loadings the design criteria for the multilayered vessels has been established. However, it can not be used to design MECVs because blast loadings are quite different from static loadings. Five MECVs with the same materials and dimensions except for steel ribbon winding angles were fabricated and tested under internal blast loading induced by centrally located TNT in order to develop design criteria. Dynamic strains at the outer surface of tested vessels were measured, and fracture characteristics also were observed, which lay a solid foundation for conducting theoretic dynamic response analysis and numerical simulation, and establishing fracture criteria.

PVP2006-ICPVT-11-93635 pp. 1485-1490; (6 pages)
doi:10.1115/PVP2006-ICPVT-11-93635

In another paper [1], the authors presented an approach to penetration of a particulate target. This theory is based on the friction that the particles of target material present to the entire penetrator surface, including its shank. The shank of the penetrator affords a very large surface area compared to that of the nose. Even modest friction acting on the shank can provide a fairly large retarding force. Normal pressure acting on the projectile is assumed to be velocity-squared dependant, as indicated by a number of methods, including cavity expansion modeling [2]. Penetration of sand and soil has been considered by numerous investigators, e.g. [3–5]. These investigations did not directly address the frictional component of the net resisting force acting on the penetrator. A series of laboratory scale penetrations tests were performed. Data from these tests was used to evaluate the parameters in the model. Fine foundry sand is a high-density medium (1960 kg/m3 ) with a small amount of friction. This contrasts the target used by the authors in [1], which had a sizable amount of friction. Results from the theory are in excellent agreement with the experiments with velocities as high as 630 m/sec.

PVP2006-ICPVT-11-93716 pp. 1491-1496; (6 pages)
doi:10.1115/PVP2006-ICPVT-11-93716

The Alekseevski-Tate equations have long been used to predict the penetration, penetration velocity, rod velocity, and rod erosion of long-rod projectiles or kinetic-energy penetrators [1]. These nonlinear equations were originally solved numerically, then by the exact analytical solution of Walters and Segletes [2, 3]. However, due to the nonlinear nature of the equations, the penetration was obtained implicitly as a function of time, so that an explicit functional dependence of the penetration on material properties was not obtained. Walters and Williams [4, 5, 6] obtained the velocities, length, and penetration as an explicit function of time by employing a perturbation solution of the non-dimensional Alekseevski-Tate equations. Algebraic equations were obtained for a third-order perturbation solution which showed excellent agreement with the exact solution of the Tate equations for tungsten heavy alloy rods penetrating a semi-infinite armor plate. The current paper employs this model to rapidly assess the effect of increasing the impact velocity of the penetrator and increasing the armor material properties (density and target resistance) on penetration. This study is applicable to the design of hardened targets.

Topics: Projectiles , Armor
PVP2006-ICPVT-11-93281 pp. 1499-1509; (11 pages)
doi:10.1115/PVP2006-ICPVT-11-93281

This paper presents a numerical and qualitative study on the expected hydrodynamic load-reducing effect of bubbly media near a volumetrically oscillating bubble. In this study, the bubble or bubble cloud is assumed to be spherically symmetric, and its motion is analyzed as a one-dimensional compressible two-phase flow in the radial direction in spherical coordinates. We adopted the CCUP (CIP-Combined Unified Procedure) method, which is a unified analysis method for both compressible and incompressible fluids proposed by Yabe et al. (1991) in order to treat interaction among gas, liquid, and two-phase media, and to avoid large numerical dissipation at density discontinuities. To verify the analysis program we developed, we analyzed free oscillations of a bubble with a unity void fraction and of a bubble cloud with an initial void fraction of 0.5, and found that the natural frequency from numerical results are well reproduced with an error of 0.9% for the bubble and 5% for the bubble cloud as compared to those obtained on a theoretical basis. Using this method, we analyzed the free oscillation of a bubble cloud in which a bubble with a unity void fraction is covered by a bubbly media layer with an initial void fraction of 0.5. Numerical results show that the amplitude of pressure oscillation inside the bubble is about halved, and that a higher mode of oscillation appears when a bubbly media layer covers the bubble. The measured results from a blowdown test we previously reported also shows a similar higher mode of oscillation. The amplitude of pressure oscillation in the water region was apparently reduced when a thick bubbly media layer covers the bubble. Thus, if the bubbly media is ejected from sparger holes prior to the ejection of a high-pressure bubble, the bubbly media might reduce the hydrodynamic load induced in a water pool made by volumetric oscillation of the bubble.

Topics: Stress , Bubbles , Water
PVP2006-ICPVT-11-93337 pp. 1511-1518; (8 pages)
doi:10.1115/PVP2006-ICPVT-11-93337

During hot functional test (HFT) of the auxiliary feedwater (AFW) system of a nuclear power plant, high vibration and noise occurred in the downstream of the cavitating venturi (CV), which caused severe damages, such as the disengagement of internal parts, failure of threaded connection to the temperature gauge located nearby downstream piping, relaxation of fastening nuts for pipe clamp and damaged socket weld connection. The objective of this paper is to evaluate the venturi downstream piping vibration in accordance with the ASME OM 3 requirements and identify the characteristics of the high frequency piping vibration. The vibration test was performed for the steam generator-operating pressure range to confirm whether the amplitudes of the vibration are within the acceptable limits to assure that no piping failures would occur due to cyclic loads. In addition to the vibration evaluation from the fatigue standpoint, the root cause of piping vibration is investigated. From the test results, the characteristics of vibration are acoustically coupled with vortex-shedding and cavitations, which results in a frequency range from 2,000 to 5,000 Hz. During the test, the vibration and noise were severer at the steam generator pressure of 40 kg/cm2 rather than at the atmospheric pressure, or even at 82 kg/cm2 . It was also detected that degrees of cavitation and locations where the collapse occurred varied depending on operating conditions. Due to the high frequency characteristics, the shell mode vibration was more dominant than the lateral beam mode vibration.

PVP2006-ICPVT-11-93396 pp. 1519-1527; (9 pages)
doi:10.1115/PVP2006-ICPVT-11-93396

Mathematical and numerical model needed for description of single-elbow pipe movement in horizontal Z-Y plane coupled with one-dimensional single-phase fluid dynamics is described and discussed. The governing phenomenon is also known as two-way Fluid-Structure Interaction. Standard Skalak’s four-equation model was improved with additional four Timoshenko’s beam equations for description of flexural displacements and rotations. The applied model was solved with improved second-order accurate numerical method that is based on Godounov’s upwind first-order accurate method. The model was successfully used for simulation of the rod impact induced transient and conventional instantaneous valve closure induced transient in the tank-pipe-valve system. Special attention was made to the applicability of the applied numerical method.

Topics: Pipes
PVP2006-ICPVT-11-93405 pp. 1529-1538; (10 pages)
doi:10.1115/PVP2006-ICPVT-11-93405

In contradiction with common assumptions of a laminar lubricant flow, it is shown that high Reynolds number lubricant flows may occur in usual metal forming processes even at scales as small as the surface roughness asperities. This enhances the sensitivity of the flow to perturbations arising e.g. from the surface roughness and brings about the possibility of a roughness-induced transition toward an unsteady flow/turbulence. Via lattice Boltzmann simulations, it is shown that, under these circumstances, a qualitative change in flow properties may indeed be triggered by a variation of the wall roughness alone. We focus on the impact of various roughness parameters on the transition showing that it is not the roughness height alone which determines the onset of flow instability. Rather, it is the combined effect of the roughness height- and wave length which is essential. In particular, by an increase of the roughness wave length, it is possible to trigger flow instability even if the roughness slope is reduced. These findings are in line with experimental results on rough wall turbulence which indicate that a local Reynolds number based on the roughness height alone does not capture the roughness effects on the flow characteristics.

PVP2006-ICPVT-11-93456 pp. 1539-1548; (10 pages)
doi:10.1115/PVP2006-ICPVT-11-93456

According to Finnish regulatory requirements, reactor internals have to stay intact in design basis accident (DBA) situations, so that control rods can always penetrate into the core. This is the basic motivation to study and develop more detailed methods for analyses of thermal-hydraulic loads on reactor internals during the DBA situation in the Loviisa Nuclear Power Plant (NPP) in Finland. In this work, the studied accident situation is Large Break Loss of Coolant Accident (LBLOCA). The objective of this work is to connect thermal-hydraulic and mechanical analysis methods with the goal to produce a reliable method for determination of thermal-hydraulic and mechanical loads on reactor internals in the accident situation. In the present model, the downcomer of a PWR is only included and the reactor internals will be added later. The tools studied are thermal-hydraulic system codes, computational fluid dynamics (CFD) codes and finite element analysis (FEA) codes. Both thermal-hydraulic and mechanical aspects are discussed in this paper. Firstly, the pressure boundary condition in the pipe break point was calculated with the system code. In the second step, CFD analyses were made. Finally, the full fluid-structure interaction coupling between the CFD and FEA codes was used. The codes used for development and simulations are APROS system code for boundary condition calculations, STAR-CD and FLUENT for CFD calculations and ABAQUS for FEA calculations.

Topics: Stress
PVP2006-ICPVT-11-93497 pp. 1549-1559; (11 pages)
doi:10.1115/PVP2006-ICPVT-11-93497

Thermal sleeves in the shape of thin wall cylinder seated inside the nozzle part of each safety injection (SI) line at pressurized water reactors (PWRs) have such functions as prevention and relief of potential excessive transient thermal stress in the wall of SI line nozzle part which is initially heated up with hot water flowing in the primary coolant piping system when cold water is injected into the system through the SI nozzles during the SI operation. Recently, mechanical failures that the sleeves are separated from the SI branch pipe and fall into the connected cold leg main pipe occurred in sequence at some typical PWR plants in Korea. To find out the root cause of thermal sleeve breakaway failures, the flow situation in the in the junction of primary coolant main pipe and SI branch pipe and the vibration modal characteristics of the thermal sleeve are investigated in details by using both computational fluid dynamic (CFD) code and structure analysis finite element code. As the results, the transient response in fluid pressure exerting on the local part of thermal sleeve wall surface to the primary coolant flow through the pipe junction area during the normal reactor operation mode shows oscillatory characteristics with the frequencies ranging from 15 to 18, which coincide with the lower mode natural frequencies of thermal sleeve having a pinned support condition on the circumferential prominence on the outer surface of thermal sleeve which is put into the circumferential groove on the inner surface of SI nozzle at the mid-height of thermal sleeve. In addition, the variation of pressure on the thermal sleeve surface yield alternating forces and torques in the directions of two rectangular axes perpendicular to the longitudinal axis of cylindrical thermal sleeve, which causes both rolling and pitching motions of the thermal sleeve. Consequently, it is seen that this flow situation surrounding the thermal sleeve during the normal reactor operation can induce resonant vibrations accompanying the shaking motion of the thermal sleeve at the pinned support condition, which finally leads to the failures of thermal sleeve breakaway from the SI nozzle.

PVP2006-ICPVT-11-93519 pp. 1561-1570; (10 pages)
doi:10.1115/PVP2006-ICPVT-11-93519

Pressure wave propagation problems in liquids have traditionally been solved using the methods of fluid transients, i.e. methods of characteristics and impedance. For gases the equations of acoustics are employed. In short pipe lines, in which friction can be ignored, the equations of fluid transients reduce into the form of the wave equation used in acoustics in a channel of constant cross-section. If the wave motion is harmonic, the one-dimensional Webster’s equation and the impedance method yield exactly the same results in tapered channels. The boundary conditions are the known pressure amplitude upstream and zero pressure at the channel outlet. These two methods have been compared for solving wave propagation problems in tapered channels used in many different industrial applications. It was found that these two methods yield exactly the same results, which are also the same as those obtained numerically with the method of characteristics. A desired quality of the tapered channel in many different industrial processes is to minimize the volume flow rate oscillation at the channel outlet. This can be achieved by changing the channel shape from the traditional linear taper, the parabolic shape giving the lowest amplitude. The effect of different quantities such as oscillation frequency and channel dimensions on volume flow rate oscillation was shown. Also, the effect of free air which affects the wave speed was studied. Since the acoustical and fluid transients approaches give identical results in a one-dimensional case, the acoustics method was employed in a three-dimensional problem, which consists of a flow spreader and a tapered channel configuration, and it was solved with the commercial FEM code Abaqus. The results show that there is a variation in the volume flow rate oscillation along the tapered channel width. The three-dimensional computational results can only be verified by measuring the velocity oscillation at the outlet of the tapered channel. The particle image velocimetry (PIV) measurements are in progress at the moment.

PVP2006-ICPVT-11-93546 pp. 1571-1575; (5 pages)
doi:10.1115/PVP2006-ICPVT-11-93546

Turbulent flow-induced vibration in nuclear fuel may cause fretting wear of fuel rod at grid support locations. An advanced nuclear fuel for Korean PWR standard nuclear power plants (KSNPs), has been developed to get higher performance comparing to the current fuel considering the safety and economy. One of the significant features of the advanced fuel is the conformal shape in mid grid springs and dimples, which are developed to diminish the fretting wear failure. Long-term hydraulic tests have been performed to evaluate the fretting wear of the fuel rod with the conformal springs and dimples. Wear volume is a measure to predict the fretting wear performance. The shapes of a lot of scars are non-uniform such as wedge shapes, and axially non-symmetric shapes, etc., depending on the contact angle between fuel rod and springs/dimples. In addition, conformal springs and dimples make wear scars wide and thin comparing to conventional ones with convex shape. It is found that wear volumes of these kinds of non-uniform wear scars are over-predicted when the traditionally used wear depth-dependent volume calculation method is employed. In order to predict wear volume more accurately, therefore, the measuring system with high accuracy has been used and verified by the known wear volumes of standard specimens. The wear volumes of the various wear scars have been generated by the measuring system and used for predicting the fretting wear-induced failure time. Based on new evaluation method, it is considered that the fretting wear-induced fuel failure duration with this conformal grid has increased up to 8 times compared to the traditionally used wear depth-dependent volume calculation method.

Topics: Wear , Shapes , Fuel rods
PVP2006-ICPVT-11-93662 pp. 1577-1586; (10 pages)
doi:10.1115/PVP2006-ICPVT-11-93662

Nowadays, the LES (Large Eddy Simulation) models have reached an advanced stage in the thermal hydraulic numerical analyses. Particularly, in the mixing tee geometry, the LES allows the thermal, temperature fluctuations cartography — both in amplitude and frequency — to be evaluated. However, for the purpose of mechanical studies a better determination of the fluctuation temperature which impacts the wall would be of significant interest, magnitude of the fluctuation being directly linked to the lifetime of the Tee. This demand steps of experimental qualifications based on cartographic comparisons between numerical and experimental results, not compatible with basic current experiments proposing only local measurements. A mixing tee mock-up (∅ 50 mm) called “the skin of the fluid” was designed to show the real time observation of the temperature fluctuations in the mixing area with a digital infrared device. With its low Biot number the mock-up is quasi permeable to the fluctuation and does not attenuate the temperature amplitude at high frequency, consequently, the infrared image represents the temperature fluctuations which impacts the wall. An existent LES numerical analysis performed with the TRIO U code (developed by the CEA) on the same geometry is shown for a first comparative approach.

Topics: Fluids , Skin
PVP2006-ICPVT-11-93689 pp. 1587-1597; (11 pages)
doi:10.1115/PVP2006-ICPVT-11-93689

A numerical study of evaluation of turbulence models for predicting the thermal stratification phenomenon is presented. The tested models are the elliptic blending model (EBM), the two-layer model, the shear stress transport model (SST) and the elliptic relaxation model (V2-f). These four turbulence models are applied to the prediction of a thermal stratification in an upper plenum of a liquid metal reactor experimented at the Japan Nuclear Cooperation (JNC). The algebraic flux model is used for treating the turbulent heat fluxes for all the models. The EBM and V2-f models predict properly the steep gradient of the temperature at the interface of the cold and hot regions which is observed in the experimental data, and the EBM and V2-f models have the capability of predicting the temporal oscillation of the temperature. The two-layer and SST models predict the diffusive temperature gradient at the interface of a thermal stratification and fail to predict a temporal oscillation of the temperature. In general the EBM predicts best the thermal stratification phenomenon in the upper plenum of the liquid metal reactor.

PVP2006-ICPVT-11-93703 pp. 1599-1612; (14 pages)
doi:10.1115/PVP2006-ICPVT-11-93703

In recent years some Boiling Water Reactors have experienced significant steam dryer cracking. In some cases this cracking has necessitated unplanned outages to implement steam dryer repairs and has also resulted in de-rated operation of the affected units. In response to these recent steam dryer failures, GE has initiated a research program focused on identifying the nature of the fluctuating loads experienced by the steam dryer and developing predictive methods that can be used to develop load definitions for steam dryers. The physical mechanisms responsible for excitation of aero-acoustic resonances are not easily modeled using purely analytic methods; therefore, GE has decided to perform model tests to investigate the nature of the expected steam dryer loading. The objectives of the study documented in this paper are to: 1) Provide guidance regarding how to preserve, in the model, the significant fluid phenomena occurring in the plant, and 2) Derive scaling laws to convert model data to plant load predictions.

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